Time–Distance Helioseismology Data Analysis Pipeline for ...sun.stanford.edu/~junwei/TD_pipeline.pdfTime-Distance Pipeline for HMI Figure 2. Typical power spectrum (k − ω) diagram

Solar PhysicsDOI: 10.1007/•••••-•••-•••-••••-•

Time–Distance Helioseismology Data Analysis Pipelinefor Helioseismic and Magnetic Imager onboard SolarDynamics Observatory (SDO/HMI) and Its InitialResults

J. Zhao1· S. Couvidat1 · R.S. Bogart1 ·

K.V. Parchevsky1 · A.C. Birch2· T.L. Duvall Jr. 3

·

J.G. Beck1 · A.G. Kosovichev1 · P.H. Scherrer1

c© Springer••••

Abstract TheHelioseismic and Magnetic Imager onboard theSolar Dynamics Obser-vatory (SDO/HMI) provides continuous full-disk observations of solar oscillations. Wedevelop a data-analysis pipeline based on the time-distance helioseismology methodto measure acoustic travel times using HMI Doppler-shift observations, and infer solarinterior properties by inverting these measurements. The pipeline is used for routineproduction of near-real-time full-disk maps of subsurfacewave-speed perturbations andhorizontal flow velocities for depths ranging from 0 to 20 Mm,every eight hours. Inaddition, Carrington synoptic maps for the subsurface properties are made from thesefull-disk maps. The pipeline can also be used for selected target areas and time periods.We explain details of the pipeline organization and procedures, including processingof the HMI Doppler observations, measurements of the traveltimes, inversions, andconstructions of the full-disk and synoptic maps. Some initial results from the pipeline,including full-disk flow maps, sunspot subsurface flow fields, and the interior rotationand meridional flow speeds, are presented.

Keywords: Sun: helioseismology; Sun: oscillations; Sun: SDO

1. Introduction

TheHelioseismic and Magnetic Imager onboard theSolar Dynamics Observatory (SDO/HMI:Schouet al., 2011) observes the solar full-disk intensity, Doppler velocity, and vec-tor magnetic field of the photosphere with high spatial resolution and high temporalcadence. Similar to theMichelson Doppler Imager (MDI: Scherreret al., 1995), an

1 W.W. Hansen Experimental Physics Laboratory, Stanford University,Stanford, CA 94305-4085, USA email:[email protected] NorthWest Research Associates, CoRA Division, 3380 MitchellLane, Boulder, CO 80301, USA3 Laboratory for Astronomy and Solar Physics, NASA Goddard SpaceFlight Center, Greenbelt, MD 20771, USA

SOLA: ms.tex; 23 March 2011; 15:27; p. 1

J. Zhaoet al.

instrument onboard theSolar and Heliospheric Observatory (SOHO), the HMI Dopp-lergrams are primarily used for helioseismic analysis to investigate the interior structureand dynamics of the Sun. Helioseismology data analysis pipelines are planned for nearreal-time analyses of the observations in order to provide the analysis results to thehelioseismology and solar physics communities. The time–distance analysis pipelineis one of the pipelines for local helioseismology studies, and other pipelines includering–diagram analysis and farside active region imaging. The time–distance pipeline isdesigned for routine production of nearly full-disk subsurface wave-speed perturbationsand horizontal flow fields every eight hours, as well as synoptic flow maps for everyCarrington rotation. It can also be used to analyze specific target areas and time periods.

Time–distance helioseismology was first introduced by Duvall et al. (1993, 1996),and it has developed rapidly since then. Different inversion techniques were introducedand tested. The LSQR algorithm, introduced by Kosovichev (1996) and used later byZhao, Kosovichev, and Duvall (2001), solves the inversion problem in a least-squaressense in the spatial domain by an iterative approach. The Multi-Channel Deconvolution(MCD) method, introduced by Jacobsenet al. (1999) and widely used in later studies(e.g. Couvidatet al., 2004), solves the least-squares problems in the Fourier domain.Later, Couvidatet al. (2005) applied a horizontal regularization procedure for thisinversion technique. More recently, an optimally localized averaging (OLA) inversionscheme was introduced to study the solar subsurface flow fields (Jackiewicz, Gizon, andBirch, 2008).

Different types of sensitivity kernels, which describe therelationship between thetravel times and interior properties, were also introducedand used in the time-distanceinversion problems. Kosovichev (1996) first used ray-path approximation kernels, Jensen,Jacobsen, and Christensen-Dalsgaard (2000) introduced Fresnel-zone kernels; and Birchand Kosovichev (2000), Birch, Kosovichev, and Duvall (2004), and Birch and Gizon(2007) investigated Born-approximation kernels for both sound-speed structures andflow fields. Couvidatet al. (2006) compared subsurface sound-speed perturbation struc-tures inferred from these different types of kernels, and found that the inversion resultsobtained with the different kernels were basically consistent.

Important results on the solar interior properties have been obtained from the time–distance studies as well as from other local helioseismology techniques. On globalscales, poleward meridional flows were found below the photosphere (Gileset al.,1997), and solar-cycle dependent meridional flow variations were also investigated anddiscussed (Chou and Dai, 2001; Beck, Gizon, and Duvall, 2002; Zhao and Kosovichev,2004). On local scales, subsurface sound-speed perturbations and flow fields were de-rived for supergranulation (Kosovichev and Duvall, 1997; Duvall et al., 1997; Du-vall and Gizon, 2000; Sekiiet al., 2007; Jackiewicz, Gizon, and Birch, 2008) and forsunspots (Kosovichev, Duvall, and Scherrer, 2000; Gizon, Duvall, and Larsen, 2000;Zhao, Kosovichev, and Duvall, 2001; Couvidatet al., 2006; Zhao, Kosovichev, andSekii, 2010). Additionally, time-distance helioseismology was used to detect the emer-gence of active regions before their appearances in the photosphere (Kosovichev, Du-vall, and Scherrer, 2000; Jensenet al., 2001; Zharkov and Thompson, 2008), to im-age large active regions on the farside of the Sun (Zhao, 2007; Ilonidis, Zhao, andHartlep, 2009), and to measure sound-speed perturbations in the tachocline (Zhaoetal., 2009). These results are important for space-weather forecasting and understanding


Time-Distance Pipeline for HMI

the mechanisms for the generation of solar magnetism. The time–distance helioseismol-ogy pipeline analyses, based on the high spatial-resolution and high temporal-cadenceobservations from HMI, will greatly advance our knowledge of the interior processesand their connections with solar activity above the photosphere.

However, one should keep in mind that the physics of solar oscillations in the tur-bulent magnetized plasma is very complicated, and that the helioseismic techniquesare still in the process of being developed. Because of limited knowledge of the wavephysics and complexity of the MHD turbulence, there may be systematic uncertaintiesin the local helioseismology inferences, particularly in strong magnetic-field regionsof sunspots. For example, Lindsey and Braun (2005a, 2005b) argued that the outgoingand ingoing travel time asymmetries observed in sunspot areas might be caused by a“shower-glass effect”. Schunkeret al. (2005) found that the inclined magnetic fieldin sunspot penumbrae might cause variations of measured acoustic travel times. Zhaoand Kosovichev (2006) found that this inclined magnetic field dependent effect doesnot exist in the measurements obtained from the MDI intensity observations. Later,Rajaguruet al. (2006) found that the non-uniform acoustic power distribution in thephotosphere also contributed to measured travel-time shifts in active regions if a phase-speed filtering procedure was applied. This effect was then studied by Parchevsky,Zhao, and Kosovichev (2008) and Hanasogeet al. (2008) numerically, and also byNigam and Kosovichev (2010) analytically. More recently, Gizon et al. (2009) deriveda sunspot’s subsurface flow fields after applying ridge filtering, and their inferred resultsdid not agree with the previously inverted results with a useof phase-speed filtering.Using high spatial-resolution observations fromHinode, Zhao, Kosovichev, and Sekii(2010) showed that the principal results on sunspot structure did not depend on theuse of phase-speed filtering. However, significant systematic uncertainties in sunspotseismology remain and need to be understood, and these are being actively studied bythe use of numerical simulations. For a recent review of the sunspot seismology anduncertainties see Kosovichev (2010).

Despite the ongoing discussions of accuracy of time–distance measurements andinterpretation of inversion results, it is useful to provide the measured travel timesand the inversion results for investigations of structuresand flows below the visiblesurface of the Sun. As the flow chart of the pipeline in Figure 1shows, we apply phase-speed filtering to the HMI data, compute cross-covariances of the oscillations, and usetwo different travel-time fitting procedures to derive the acoustic travel times. We thenperform inversions using two different sets of travel-timesensitivity kernels, based onthe ray-path and Born approximations, to infer subsurface wave-speed perturbations andflow fields, using the MCD inversion method. We provide onlineaccess to the measuredtravel times, full-disk subsurface wave-speed perturbations and flow maps calculatedevery eight hours. In addition, we provide synoptic flow mapsfor each Carringtonrotation. In this article, we describe details of the acoustic travel time measurementprocedure in Section 2, and the inversion procedure in Section 3. We describe thepipeline data products and present initial HMI results in Section 4, and summarize ourwork in Section 5.


J. Zhaoet al.

Figure 1. Flow chart for the HMI time-distance helioseismology data analysis pipeline.

2. Acoustic Travel-Time Measurement

2.1. Tracking and Remapping

The SDO/HMI continuously observes the full-disk Sun, providing Doppler velocity,continuum intensity, line-depth, line-width, and magnetic field maps with a 45-secondcadence, and also vector magnetic field measurements with a cadence of 12 minutes.Each full-disk image has4096 × 4096 pixels with a spatial resolution of 0.504 arcsecpixel−1 (i.e., approximately, 0.03 heliographic degree pixel−1 at the solar disk center).The Doppler observations are primarily used for helioseismic studies. The observ-ing sequences, algorithms for deriving Doppler velocity and magnetic field, and otherinstrument calibration issues are discussed by Schouet al. (2011).

As illustrated in Figure 1, the primary input for the pipeline is Dopplergrams, al-though in principle, the HMI intensitygrams and line-depthdata can also be analyzed inthe same manner. Users of the pipeline can select specific areas for analysis, preferablywithin 60◦ from the solar disk center. In practice, the users provide the Carringtonlongitude and latitude of the center of the selected area, and the mid-time of the selectedtime period, then the pipeline code selects an area of roughly 30◦ × 30◦ centered at thegiven coordinate, and for a time interval of eight hours withthe given time as the middlepoint. The data for this selected area and the time period arethen tracked to remove solarrotation, and remapped into the heliographic coordinates using Postel’s projection (alsoknown as azimuthal equidistant projection) relative to thegiven area center. Normally,the tracked area consists of512 × 512 pixels with a spatial sampling of0.06◦ pixel−1;and the temporal sampling is the same as the observational cadence. Cubic interpolationis used for the pixels not located on the observational grid.

Figure 2 shows typical HMIk–ω and time–distance diagrams obtained from onetracked and remapped area. The selected area covers30◦ in latitude and has an apparent



Figure 2. Typical power spectrum (k − ω) diagram (upper) and time–distance (cross-covariance) diagram(lower) made from eight hours of HMI Doppler observations.

differential rotation over this span. However, for fast computations, only one uniform

tracking rate corresponding to the Snodgrass rotation rateat the center of this area is

used. The Snodgrass rotation rate is:2.851−0.343 sin2 φ−0.474 sin4 φ µrad s−1, where

φ is latitude (Snodgrass and Ulrich, 1990). The uniform tracking rate of the selected area

results in a differential rotation velocity in the invertedhorizontal velocity fields. This

differential rotation velocity is removed from the full-disk flow maps after averaging

over the whole Carrington rotation, and only the residual flow fields are given as the

final results (see Section 4.1). But for the user-selected areas, the differential rotation is

kept in the inversion results.


J. Zhaoet al.

Table 1. Phase-speed filtering parameters used for the selected traveldistances (annulus ranges).

annulus No. annulus range phase speed FWHM(heliographic degree) (µHz/ℓ) (µHz/ℓ)

1 0.54 – 0.78 3.40 1.02 0.78 – 1.02 4.00 1.0

3 1.08 – 1.32 4.90 1.254 1.44 – 1.80 6.592 2.1495 1.92 – 2.40 8.342 1.3516 2.40 – 2.88 9.288 1.1837 3.12 – 3.84 10.822 1.8958 4.08 – 4.80 12.792 2.0469 5.04 – 6.00 14.852 2.075

10 6.24 – 7.68 17.002 2.22311 7.68 – 9.12 19.133 2.039

2.2. Computing Cross-Correlations and Fitting for Travel Times

Each tracked and remapped Dopplergram datacube is filtered in the 3D Fourier domain.Solar convection andf -mode oscillation signals are removed first, and then phase-speedfiltering is applied following the procedures prescribed byCouvidatet al. (2005). Forthe travel-time measurements, for each central point we select 11 annuli with vari-ous radii and widths chosen from our past experience with MDIanalyses. All of thephase-speed filtering parameters, including the central phase-speed, filter width, and thecorresponding inner and outer annulus radii are presented in Table 1. The phase-speedfilter is a Gaussian function of the wave’s horizontal phase speed. It selects wave pack-ets traveling between the central points and the annuli for the selected distances. Thisfilter helps improve the signal-to-noise ratio, and also removes leakage from low-degreeoscillations. After the filtering, the data are transformedback to the space–time domainfor cross-covariance computations. Two different fitting methods are used to derive theacoustic travel times from the cross-covariances: a Gabor wavelet fitting (Kosovichevand Duvall, 1997), and a cross-correlation method based on seismology algorithms(Zhao and Jordan, 1998) adopted by Gizon and Birch (2002; GB algorithm hereafter).A detailed description of the filtering procedure, the cross-covariance computations, thetwo types of travel-time fittings, comparison of the travel times derived from the twofitting methods, and the measurement error estimates is given by Couvidatet al. (2011).In particular, it has been shown there that the two definitions of the acoustic travel timesand the two fitting methods give generally consistent results in the quiet-Sun regions,but may give different results in active regions. The differences are currently not wellunderstood, but in the pipeline we implement both travel-time definitions.

In the Postel-projected maps, the exact distance between two arbitrary points cannotbe calculated using the Cartesian coordinates. Thus, when an annulus is selected arounda given location, some additional computations are needed to determine the exact great-circle distance between the points. The formula to determine the great-circle distance



is:

∆ = arccos(sin θ1 sin θ2 + cos θ1 cos θ2 cos(φ1 − φ2)), (1)

where(θ1, φ1) and(θ2, φ2) are the heliospheric longitude and latitude coordinates forthe two separate locations.

To facilitate the inversions for subsurface flow fields, eachannulus is divided intofour quadrants representing the North, South, East, and West directions (Kosovichevand Duvall, 1997). So, for each annulus and each travel-timefitting method, we obtainsix measurements of acoustic travel times, corresponding to the outgoing and ingoing,East-, West-, South-, and North-going directions. We then combine these travel times toobtain one map for the mean travel time and three maps for the travel-time differences.These travel times are:τmean (average of outgoing and ingoing travel times),τoi (dif-ference of outgoing and ingoing travel times),τwe (difference of West- and East-goingtravel times), andτns (difference of North- and South-going travel times). Thesefourtravel-time maps for each annulus are archived and available through the HMI DataRecord Management System (DRMS).

3. Subsurface Wave-Speed Perturbation and Flow Field Inversions

The acoustic travel times are derived by two different fitting methods: the Gabor waveletfunction and the GB algorithm. Then, as illustrated in Figure 1, to infer the subsurfacewave-speed perturbations and flow velocities, the Gabor-wavelet travel times are in-verted using the ray-path approximation sensitivity kernels, and the GB travel timesare inverted using the Born-approximation sensitivity kernels. The Born-approximationkernels are calculated based with the filter and window parameters of the GB fits.

3.1. Inversions

Both the ray-path and Born-approximation kernels have beenused in previous time–distance studies (e.g. Zhao, Kosovichev, and Duvall, 2001; Couvidatet al., 2006).Details of the kernel calculations and their comparisons will be given in a separatepaper.

We employ the MCD inversion method (Jacobsenet al., 1999) with a horizontalregularization (Couvidatet al., 2005). For the wave-speed perturbation inversions, thelinearized equation relating the measured mean travel times and the subsurface wave-speed perturbations are:

δτλµνmean

=∑

ijk

Aλµνijk δsijk, (2)

whereδsijk is the relative wave-speed perturbationδcijk/cijk approximated by piece-wise constant functions on the inversion grid, andAλµν

ijk is a matrix of the discretizedsensitivity kernel. Here,λ andµ label the coordinates of the central points of the annuliin the observed areas,ν labels the different annuli, andi, j, andk are the indices for thediscretized three-dimensional space for inversions. Usually, the horizontal coordinatesof the inversion grid (i andj indices) are selected at the same locations as the centraltravel-time measurement points (λ andµ indices). In the first-order approximation, the


J. Zhaoet al.

sensitivity kernels are calculated for a spherically symmetric solar model and do notdepend on the position on the solar surface. Therefore, in this case Equation (2) isactually equivalent to a convolution in the horizontal domain, which can be simplifiedas a direct multiplication in the Fourier domain:

δτν(κλ, κµ) =∑

k

Aνk(κλ, κµ)δsk(κλ, κµ), (3)

whereδτ , A, andδs are the 2D Fourier transforms ofδτ , A, andδs, respectively;kis the same as in Equation (2);κλ andκµ are the wavenumbers in the Fourier domaincorresponding toλ andµ of the spatial domain. For each(κλ, κµ), the equation in theFourier domain is a matrix multiplication:

d = Gm, (4)

where

d ={

δτν(κλ, κµ)}

, G ={

Aνk(κλ, κµ)

}

, m ={

δsk(κλ, κµ)}

.

Thus, we have a large number of linear equations describing the depth dependence ofthe Fourier components, and each linear equation can be solved in the least squaressense. After all these equations are solved, andm is obtained for each(κλ, κµ), thevalues ofδsijk are calculated by the inverse 2D Fourier transform.

Equation (4) is ill-posed, and regularization is required to obtain a smooth solution.The regularized least-squares algorithm is formulated as:

min{

‖(d − Gm)‖2

2+ λ2(κ)‖Lm‖2

2

}

, (5)

where‖...‖2 denotes the L2-norm,L is a regularization operator, andλ(κ) is a reg-ularization parameter. We chooseL to be a diagonal matrix whose elements are theinverse of the square root of the spatial sampling∆z at each depth. Such weightingis necessary because the grid in the vertical direction is chosen to be approximatelyuniform in the acoustic depth, meaning that the spatial sampling of deep layers is largerthan the sampling of shallower layers. The regularization parameter is taken in the formof λ2(κ) = λ2

v + λ2

h(κ), whereλv andλh are vertical and horizontal regularization pa-rameters. The purpose of introducingλh is to damp the high wavenumber componentsthat may lead to noise amplification. Following the discussion of Couvidatet al. (2005),we chooseλh = λ2κ

2 with λ2 as a constant.Because the regularization is applied in the Fourier domain, it is quite difficult to

use different regularization parameters for different horizontal locations of the sameregion. Sometimes, different regularization parameters are needed because in activeregions the noise level may be different from the quiet-Sun regions, as we discuss inSection 3.3. Thus, it is necessary to implement into the analysis pipeline another inver-sion technique, the LSQR algorithm, which solves Equation (2) in the space domain byan iterative approach. This implementation is currently under development.



Table 2. Measured mean travel times and uncertainties for both quietSun regions and active regions.

annulus No. mean travel time uncertainty for quiet regions uncertainty for active regions(min) (min) (min)

1 11.87 0.062 0.17

2 18.82 0.061 0.253 21.76 0.11 0.264 25.85 0.11 0.195 28.69 0.14 0.156 31.18 0.14 0.147 35.07 0.10 0.10

8 38.86 0.12 0.119 42.46 0.11 0.09310 46.63 0.14 0.1111 50.26 0.15 0.11

3.2. Inversion Depth and Validation of Inversions

For both the wave-speed and flow-field inversions, and for both the ray-path and Born-approximation inversions, we select a total of 11 inversiondepths as follows: 0 – 1,1 – 3, 3 – 5, 5 – 7, 7 – 10, 10 – 13, 13 – 17, 17 – 21, 21 – 26, 26 – 30, and 30 – 35Mm. There is a total of 11 depth intervals. The inversion results provide the wave-speedperturbations and flow velocities averaged in these layers.Due to the lack of acousticwave coverage in the deep interior, the reliability of inversion results decreases with thedepth. Thus, only inversion results for the depths shallower than 20 Mm are included inthe pipeline output. This may change in the future when more confidence is gained inthe deeper interior inversion results.

In recent years, several studies have been carried out to validate the time–distancemeasurements and inversions. To validate the derived subsurface flow fields, Geor-gobianiet al. (2007) and Zhaoet al. (2007) have analyzed realistic solar convectionsimulations and found satisfactory inversion results for the shallow layers covered bythe simulations. Validations of the wave-speed perturbation inversions based on numeri-cal simulations with preset structures have also been performed. Meanwhile, numericalsimulations for magnetic structures with flows are also under development (Rempel,Schussler, and Knolker, 2009; Steinet al., 2011; Kitiashviliet al., 2011). Validationsof the time-distance helioseismology techniques will be carried out as well using thesesimulations.

Cross-comparisons between different helioseismology techniques,e.g. comparingthe mean rotation speed from our pipeline analysis with global helioseismology results,and comparing the subsurface flow fields with results from ring-diagram analyses, willalso be important for the validation.

3.3. Error Estimate

There are two types of errors in the pipeline results: systematic errors due to our limitedknowledge of the wave physics in the magnetized turbulent medium and simplified


J. Zhaoet al.

Table 3. Error estimates for the relative wave-speed perturbation and horizontal velocityinferences in the quiet-Sun (QS) and active regions (AR).

Depth wave speed for QS velocity for QS wave speed for AR velocity for AR(Mm) (m s−1) (m s−1)

0 – 1 2.8 × 10−3 7.8 6.3 × 10−3 58.31 – 3 4.1 × 10−3 7.5 10.9 × 10−3 56.4

3 – 5 6.4 × 10−3 8.9 8.7 × 10

−3 51.15 – 7 4.6 × 10

−3 9.4 9.7 × 10−3 45.1

7 – 10 4.7 × 10−3 13.1 6.7 × 10

−3 34.510 – 13 3.7 × 10−3 12.9 3.1 × 10−3 28.1

mathematical formulations, and statistical errors, whichare mostly due to the stochasticnature of the solar oscillations (“realization noise”). Here, we only discuss the statisticalerrors.

To estimate the errors in the inversion results, we need firstto estimate the uncertain-ties in the measured acoustic travel times. Here, we estimate the measurement uncer-tainties following the prescriptions of Jensenet al. (2003) and Couvidatet al. (2006).We select 25 quiet-Sun regions, and use the rms variation of mean travel times fordifferent measurement distances as an error estimate for the travel times. The estimateduncertainties for the Gabor wavelet fitting are given in Table 2, and the uncertaintiesobtained for the GB algorithm are similar, but slightly larger for short distances andslightly smaller for long distances. Active regions have different measurement uncer-tainties. To estimate these, we selected a relatively stable sunspot, NOAA AR 11092,from 2 through 5 August 2010, and we assumed that the sunspot did not change duringthis period. Then we use the rms of the travel times measured inside the sunspot as anerror estimate. Due to the evolution of the sunspot, this approach overestimates the mea-surement uncertainties, but can still give us an approximate estimate of measurementerrors. These error estimates are presented in Table 2 as well.

Inversions are then performed for the same quiet-Sun regions and the active regionto estimate the statistical errors in inversion results. Following the same approach, therms of inverted wave-speed perturbations is assumed as the statistical error. The errorestimates for both the quiet Sun and active regions are shownin Table 3. Becausesupergranular flows are dominant in the flow fields, it is difficult to estimate errors of theinverted velocity for the quiet Sun by this approach. Instead, we estimate the velocityerrors based on the rotational velocity profile, which has little change in a time scaleof a few days. While the errors for the wave-speed perturbation inside active regionsare roughly twice of those for the quiet-Sun regions, the velocity errors inside activeregions sometimes are seven times larger than the errors in the quiet Sun.

4. Data Products and Initial Results from HMI

The time–distance data analysis pipeline is used for the routine production of nearlyreal-time full-disk (actually, nearly full-disk coveringa 120◦ × 120◦ area on the solardisk) wave-speed perturbation and flow field maps every eighthours. These maps are



Figure 3. Schematic plot showing how areas are selected for a routine calculations of the full-diskwave-speed and flow maps. Not all of the 25 selected areas are shown.

then used to construct the corresponding synoptic maps for each Carrington rotation.The pipeline can also be used for specific target areas, such as active regions. In thissection, we introduce the data products from this pipeline and some initial results fromit.

4.1. Routine Production: Full-Disk and Synoptic Maps

For each day of HMI observations, we select three eight-hourperiods: 00:00 – 07:59UT, 08:00 – 15:59 UT, and 16:00 – 23:59 UT. For each analysis period, we select 25regions, with the central locations at0◦,±24◦, and±48◦ in both longitude and latitude,where the longitude is relative to the central meridian at the mid-time of the selectedperiod. Figure 3 shows locations of these areas on the solar disk. The total number ofareas is 25: five rows and five columns. Due to the Postel’s projection, the boundariesof these areas are often not parallel to the latitude or longitude lines. It is also evidentthat many areas overlap, some areas overlap twice, and some overlap four times. Thetravel times and inversion results are averaged in these overlapped areas. However, inthe areas close to the solar limb, the foreshortening effectmay become non-negligible,but the role of this is not yet systematically studied. Usersof these maps are urged tobe cautious when using the pipeline results in the areas close to the limb.

For each full-disk map and each synoptic map, the East – West velocity [vx], theNorth – South velocity[vy], and wave-speed perturbation[δc/c] in each depth layer are


J. Zhaoet al.

Figure 4. A map of horizontal flow divergence for a depth range of 1 – 3 Mm and a time period of 00:00– 07:59 UT 19 May 2010. The display scale is from−6.2 × 10−4 to 6.2 × 10−4 s−1. White areas withpositive divergence correspond to supergranulation. Notethat supergranules appear larger at high latitudesbecause of the rectangular longitude–latitude map projection.

derived with a horizontal spatial sampling of0.12◦ pixel−1. For each of the 25 areas, theinversion results are first obtained in the Postel-projection coordinates, and then con-verted into the longitude–latitude coordinates. This coordinate conversion is basicallythe inverse procedure of transforming the observed data into the Postel-projection coor-dinates for the travel-time measurements. Cubic spline interpolation is employed. Theresults in high latitude regions are oversampled. After thecoordinate transformation, theoverlapped areas are averaged, and the final statistical errors are estimated for the wholeprocedure starting from the travel-time measurements. This includes all potential errorsfrom the interpolation and remapping. The final full-disk results are saved on a uniformlongitude–latitude coordinate grid, so each horizontal image of the subsurface layershas a total of1000 × 1000 pixels covering120◦ in both longitudinal and latitudinaldirections. This coordinate choice is convenient for merging and analyzing results, butunavoidably distorts maps in high latitude areas.

Figure 4 shows an example of a full-disk map of the subsurfacehorizontal flowdivergence calculated fromvx andvy at the depth range of 1 – 3 Mm. The positivedivergence areas correspond to supergranulation. Such maps at various depths with



Figure 5. A sample of subsurface horizontal flow fields with full spatial resolution at the depth of 0 – 1Mm. This area is sampled at the center of the map shown in Figure 4. The background image shows theline-of-sight magnetic field measured by HMI, with red as positive and blue as negative polarities. The rangeof the magnetic field is from−80 to 80 Gauss.

Figure 6. Synoptic map of large-scale horizontal flows at the depth of1 − 3 Mm for CR 2097. The back-ground image is the corresponding line-of-sight magnetic field, with red as positive and blue as negativepolarities, in the range of−50 to 50 Gauss.


J. Zhaoet al.

Figure 7. Averaged rotation (upper) and meridional flow speeds (lower) at selected depths for CarringtonRotation 2097. The rotation speed is relative to the constant Carrington rotation rate.

continuous temporal coverage can be valuable for studying the structure and evolutionof the supergranulation. Figure 5 displays the subsurface horizontal flow fields with fullspatial resolution for a region located at the center of the map in Figure 4. Supergranularflows can be easily identified.

From the full-disk wave-speed perturbation and flow maps obtained every eighthours, we select an area13.2◦ wide in longitude,i.e. −6.6◦ to 6.6◦ from the centralmeridian, to construct the synoptic wave-speed perturbation and flow maps. Since theCarrington rotation rate corresponds to a shift of approximately4.4◦ every eight hours,each location in the constructed synoptic maps is averaged roughly three times (i.e. onewhole day). The resultant synoptic map for each depth consists of3000 × 1000 pixels.Since such a map is difficult to display, we show in Figure 6 a binned-down synopticlarge-scale flow map obtained for the depth of1 − 3 Mm for Carrington Rotation 2097during the period from 20 May to 16 June, 2010. The vectors in the figure are obtainedby averaging the flow fields in areas of15◦ × 15◦ with a 3◦ sampling rate. The mapsof this type are similar to the subsurface flow maps obtained from the ring-diagram



Figure 8. Subsurface flow fields of AR 11072 at the depth of1 − 3 Mm, obtained from 16:00 – 23:59 UT23 May 2010. The background image is line-of-sight magneticfield, with red positive and blue negative. Theimage is displayed with a scale from−1000 to 1000 Gs. The arrows are displayed after a2 × 2 rebinning,and the longest arrow represents a speed of 300 m s−1.

analysis (Haberet al., 2002). From Figure 6, it can be found that the large-scale flowsoften converge around magnetic regions.

Normally, the full-disk flow maps and the synoptic flow maps are provided as resid-ual flow maps after subtracting the flows averaged over the entire Carrington rotation.The subtracted average maps contain the differential rotation, meridional flows, andpossibly some systematic effects. Figure 7 shows examples of the subsurface differen-tial rotation speed and meridional flow speed obtained by averaging the calculationsfor Carrington Rotation 2097. These results are also provided online together with thesynoptic flow maps.

4.2. Target Areas

As already mentioned in Section 2, the pipeline can also be run for specific target areasand specific time intervals. The pipeline users are requiredto provide the Carringtoncoordinates of the center of the target area, and the mid-time of the time interval.

Figure 8 shows an example of a small part (approximately 1/9)of a target area, withan active region, AR 11072, included in it. The subsurface flow field, at the depth of1 − 3 Mm, is displayed after a2 × 2 rebinning. The displayed time period, 16:00 –23:59 UT on 23 May 2010, is approximately 2.5 days after the start of emergence ofthis active region that was still growing. Our results clearly show subsurface outflows


J. Zhaoet al.

around the leading sunspot, and some converging flows insideit. Comparing with theprevious results of Kosovichev (2009) and Zhao, Kosovichev, and Sekii (2010), onemay conclude that the subsurface flow fields of active regionsevolve with the evolutionof active regions. There may be prominent outflows around sunspots during their earlygrowing phase and also their decaying phase, but there may also be strong convergingflows during the stable period. Our continuous monitoring ofthe solar full-disk sub-surface flows may give us an opportunity to statistically study the changes of sunspot’ssubsurface flows with the sunspot evolution.

5. Summary

We have developed a time–distance helioseismology data analysis pipeline for SDO/HMIDoppler observations. This pipeline performs acoustic travel-time measurements basedon two different methods, and conducts inversions based on two different sensitivitykernels calculated in the ray-path and Born approximations. The pipeline gives nearlyreal-time routine products of full-disk wave-speed perturbations and flow field mapsin the range of depth 0 – 20 Mm every eight hours, and provides the correspondingsynoptic wave-speed perturbation and flow field maps for eachCarrington rotation.The averaged rotation speed and meridional flow speed are also provided separately foreach rotation. In addition to these routine production, thepipeline can also be used foranalysis of specific target areas for specific time intervals. This data analysis pipelinewill provide important information about the subsurface structure and dynamics on bothlocal and global scales, and its continuous coverage through years to come will be usefulfor understanding the connections between solar subsurface properties and magneticactivity in the chromosphere and corona. With the improvement of our understanding ofacoustic wave and magnetic field interactions, and also the measurement and inversiontechniques, the pipeline codes will be regularly revised.

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Documents

Time–Distance Helioseismology Data Analysis Pipeline for ...sun.stanford.edu/~junwei/TD_pipeline.pdfTime-Distance Pipeline for HMI Figure 2. Typical power spectrum (k − ω) diagram